Calculus Examples

$2 \sqrt{x} \cdot (2 \sqrt{x})$

Step 1

Multiply $2 \sqrt{x} (2 \sqrt{x})$ .

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Step 1.1

Multiply $2$ by $2$ .

$4 \sqrt{x} \sqrt{x}$

Step 1.2

Raise $\sqrt{x}$ to the power of $1$ .

$4 ({\sqrt{x}}^{1} \sqrt{x})$

Step 1.3

Raise $\sqrt{x}$ to the power of $1$ .

$4 ({\sqrt{x}}^{1} {\sqrt{x}}^{1})$

Step 1.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 {\sqrt{x}}^{1 + 1}$

Step 1.5

Add $1$ and $1$ .

$4 {\sqrt{x}}^{2}$

Step 2

Rewrite ${\sqrt{x}}^{2}$ as $x$ .

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Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

$4 {(x^{\frac{1}{2}})}^{2}$

Step 2.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$4 x^{\frac{1}{2} \cdot 2}$

Step 2.3

Combine $\frac{1}{2}$ and $2$ .

$4 x^{\frac{2}{2}}$

Step 2.4

Cancel the common factor of $2$ .

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Step 2.4.1

Cancel the common factor.

$4 x^{\frac{2}{2}}$

Step 2.4.2

Rewrite the expression.

$4 x^{1}$

Step 2.5

Simplify.

$4 x$